But United had plenty in reserve after seeing off an Everton team that, without injured leading scorers Tim Cahill and Andrew Johnson, offered little in way of response after falling behind.

With Premier League rules rendering on-loan Tim Howard ineligible to play against his parent club, Richard Wright was handed his first league start of the season in goal for Everton.

Everton’s only other change from the team that drew at the Valley on Saturday saw centre-back Alan Stubbs replace Simon Davies in the starting line-up, Joseph Yobo moving across to right-back as Phil Neville stepped into centre midfield.

If that was indicative of Moyes’ slender resources at present, Sir Alex Ferguson demonstrated United’s strength in depth by making five changes from their weekend showdown against Chelsea.

Although Everton had lost 21 of their 28 previous Premiership meetings with United, they had been beaten only once in the last four and earned consecutive draws at Old Trafford in the past two seasons.

The kick-off was delayed a few minutes as United were handed yet more baubles in recognition of their fine start to the season, Cristiano Ronaldo named the Fans’ Player of the Month award for October while Ferguson and Paul Scholes were presented with their official monthly gongs as the Premiership’s top manager and player respectively.

Everton, though, were in no mood for such deference and, effectively employing James McFadden to roam behind lone striker James Beattie, were the more threatening side as the much-changed United struggled to find their bearings in the first half-hour.

Leon Osman was allowed early on to run unopposed from the halfway line before launching a 25-yard shot safely fielded by Edwin van der Sar, and was then involved as the visitors created the first genuine opening on 16 minutes.

An alert McFadden caught Michael Carrick napping in midfield and, after the United man had tracked back to challenge on the edge of the area, Osman fed the ball swiftly left to his Scotland international team-mate who flashed an angled drive across van der Sar’s goal.

It seemed to briefly rouse United and, after Kieran Richardson’s ambitious curling free-kick from the right clipped the top of the crossbar, Rooney glance a Mikael Silvestre cross wide of Wright’s left-hand post.

But Everton were growing in confidence as the Old Trafford faithful began showing signs of frustration at the home team, Stubbs twice having efforts blocked at the far post from a Mikel Arteta corner while van der Sar clutched a firm Beattie header.

However, six minutes away from deservedly going in level at half-time, Moyes’ side fell behind. There was an element of fortune as Carrick’s 20-yard drive was charged down by Nuno Valente into the path of Ronaldo, but nothing lucky about the finish of the Portugal international, who lashed a low drive that swerved away from the despairing dive of Wright.

The Everton goalkeeper then turned a Rooney effort behind at his near post as United, lifted by the goal, finished the half the stronger.

The magnitude of Everton’s second-half task was brought into sharp focus by the fact they hadn’t won in five previous away Premiership games since their only success on the road at Tottenham Hotspur in August, and had gone almost two years since winning a game in which they’d fallen behind.

And a bench consisting of centre-back David Weir, the lesser-spotted Andy van der Meyde and inexperienced strike duo Victor Anichebe and James Vaughan, suggested inspiration would have to come from the players already on the field.

Worryingly for Moyes, there was precious little forthcoming as United commanded the second half.

The biggest cheer of the night from the travelling support came when a strong challenge from Phil Neville left Rooney writhing around the turf, although moments later the ex-Everton striker riled his former adoring faithful by making a show of clutching the badge on his shirt.

And he upset them further on 63 minutes with a part in United’s second goal.

Accepting a pass from Carrick, Rooney fed the ball left to the onrushing left-back Evra who, unmarked having left Yobo trailing, cut inside the box before firing an angled shot that went in through the luckless Wright’s legs.

It took Moyes until 14 minutes from time before changing things, introducing young Vaughan from the bench into a centre-forward role alongside the increasingly isolated Beattie.

But United, although by now stepping down the gears, were in total control, Ferguson giving both Ronaldo and Michael Carrick a breather for the final quarter.

Yobo headed over from an Arteta corner late on, but O’Shea’s 89th-minute finish from Evra’s pass sealed an emphatic victory.